(x-3)(5x+10)=0

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Solution for (x-3)(5x+10)=0 equation:


Simplifying
(x + -3)(5x + 10) = 0

Reorder the terms:
(-3 + x)(5x + 10) = 0

Reorder the terms:
(-3 + x)(10 + 5x) = 0

Multiply (-3 + x) * (10 + 5x)
(-3(10 + 5x) + x(10 + 5x)) = 0
((10 * -3 + 5x * -3) + x(10 + 5x)) = 0
((-30 + -15x) + x(10 + 5x)) = 0
(-30 + -15x + (10 * x + 5x * x)) = 0
(-30 + -15x + (10x + 5x2)) = 0

Combine like terms: -15x + 10x = -5x
(-30 + -5x + 5x2) = 0

Solving
-30 + -5x + 5x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-6 + -1x + x2) = 0

Factor a trinomial.
5((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-2 + -1x)' equal to zero and attempt to solve: Simplifying -2 + -1x = 0 Solving -2 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + -1x = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1x = 0 + 2 -1x = 0 + 2 Combine like terms: 0 + 2 = 2 -1x = 2 Divide each side by '-1'. x = -2 Simplifying x = -2

Subproblem 2

Set the factor '(3 + -1x)' equal to zero and attempt to solve: Simplifying 3 + -1x = 0 Solving 3 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + -1x = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -1x = 0 + -3 -1x = 0 + -3 Combine like terms: 0 + -3 = -3 -1x = -3 Divide each side by '-1'. x = 3 Simplifying x = 3

Solution

x = {-2, 3}

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